7. Solve the following initial-value problems. (a) dxdy=(1−y)(2−y),y(0)=0. (b) cosydxdy=1+x2−xsiny,y(1)=π/2

(a) Given IVP as dy/dx=(1-y)(2-y) and y(0)=0 which is a variable separable form and can be written as

Resuelto 7. Solve the following initial-value problems. (a)

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Pregunta: 7. Solve the following initial-value problems. (a) dxdy=(1−y)(2−y),y(0)=0. (b) cosydxdy=1+x2−xsiny,y(1)=π/2

Muestra el texto de la transcripción de la imagen
Hay 2 pasos para resolver este problema.
Solución
Paso 1
(a) Given IVP as
$\frac{d y}{d x} = (1 - y) (2 - y) and y (0) = 0$
which is a variable separable form and can be written as
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Paso 2
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Respuesta
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Texto de la transcripción de la imagen:

7. Solve the following initial-value problems. (a)

\frac{d y}{d x} = (1 - y) (2 - y), y (0) = 0.

(b)

cos y \frac{d y}{d x} = \frac{- x s i n y}{1 + x ^{2}}, y (1) = π /2